Xun Yu's death is more forced suicide then execution so rules on that would be different.

There are exceptions like Lu Bu's strangulation or the Ma Yuanli chariot thing but I imagine most executions were beheading.

. it's said he was captured, and than Sun Quan asked him to surrender, to which he refused. Others say that Lu Meng ordered his execution the moment he was captured. If you ask me , Chances are Lu Meng captured him, executing him on the spot. I believe this because if Lu Meng was in Jing province at the time, to escort Guan Yu over to Sun Quan would have taken quite some time.

Some officers would be executed on the spot for betraying their master. Chen Gong was originally under Cao Cao. I believe he guarded Pu Yang? He helped Lu BU take over it from within. When Lu Bu was defeated , Cao Cao ordered his execution. The novel story of him trying to persuade Chen Gong to rejoin is fictional. Great story though.

Pei says Guan Yu would have been executed immediately

Chen Gong had helped Cao Cao persuade the local leaders of Yan to follow him and that death scene is actually history based

“You, are a rebellious son who abandoned his father. You are a cruel brigand who murdered his lord. How can Heaven and Earth put up with you for long? And unless you die soon, how can you face the sight of men?”

I assume by that he means Cao Cao's concerns that Liu Bei's ambition and ability to rise to top. There is a common theme after Liu Bei leaves Xu "Liu Bei asks to join so and so. So and so's court is divided: on one hand Liu Bei has army and is a famed commander. On other hand, nobody trusts him to stay loyal". Zhou Yu considered a gilded prison plan for Liu Bei as an example.

Is it true that Cheng Yu and Wei officials praised Guan Yu and Zhang Fei as comparable to 10000 men?

If true, what made them praise Guan and Zhang in the first place?

Frrom Zhang Fei's sgz

In the beginning, Zhang Fei was deemed to be inferior to Guan Yu despite his strength and might, but Wei advisors like Cheng Yu claimed that Guan Yu and Zhang Fei were “capable of fighting ten thousand men”.

We don't know what moment or argument brought on Cheng Yu's comment but one assumes their times with or fighting Wei was enough for Cheng Yu to feel confident in that

“You, are a rebellious son who abandoned his father. You are a cruel brigand who murdered his lord. How can Heaven and Earth put up with you for long? And unless you die soon, how can you face the sight of men?”

In my opinion the blame here goes to the fact that much of what happened in the time period went unrecorded or the records didn't survive. If you look at Liu Bei's biography and compare it to Zhang Fei's or Guan Yu's you will notice that Liu Bei's is like 8 times longer then either of the other 2. Now he didn't live that much longer then they did so it makes sense to believe that much of what they did just has been forgotten. At the time hey had grand reputations and were known and respected by their contemporaries. Sadly not enough has survived for us to know exactly what they knew.

It is possible that even though early in their careers they lost battles they could have vastly outnumbered yet fought fiercely causing heavy casualties despite losing thus being given reputations of being powerful. We will never really know how they gained their reputations sadly.

"If you can't drink a lobbyist's whiskey, take his money, sleep with his women and still vote against him in the morning, you don't belong in politics."

There are gaps in their careers, like their early campaign with Zou Jing and their service under Tian Kai against Yuan Tan which we know very little about. Whilst we know those campaigns happened they weren't considered significant enough for specific details of individual battles to be recorded in the histories. However I expect they earned a reputation for valour and fighting capacity during the many battles and skirmishes they likely featured in during that time.

Interested in the history behind the novel? Find a list of english language Three Kingdom sources here.

Agree with the others. Even in the larger kingdoms, one can get noted generals with reputations but little recorded deeds. One gets it with "other" kingdoms like Yuan Shao has quite a few famous generals whose sole moment we see them is their defeat (Chunyu Qiong probably the big name of that). In essence, those figures slip through gaps in our historical knowledge and for some Shu figures, pre invasion of Yi seems to have similar large gaps.

If one reads Zhang Fei's SGZ it goes "meets new friends,Chang Ban stand" and Zhang Fei does nothing else till invasion of Yi. Add from what we know from other parts, there is Xu riots, kidnap+marriage and a murder. Now it is entirely possible that for most of the pre invasion of Yi, Zhang Fei did little but play cards during battle or fight with little of note but piggyback fame off Liu Bei's record and only till the attack on Yi did he really begin an impressive miliatry career (which would be after Cheng Yu went into semi-retirement). I think we can say that is however extremely unlikely. I think we can reasonably assume, 1) Liu Bei used his military officers in his battles across the north and the centre of China, 2) during those battles they did stuff (acts of strength, handling their troops well in battle and so on) that earnt them a reputation that spread, 3) men like Cheng Yu, Cao Cao, Zhou Yu saw with their own eyes these men in battle and what they saw impressed them even to the extent of basing policy around it, 4) men noted for their ability to judge talent didn't all have a collective mental collapse when it came to Zhang Fei but Zhang Fei actually did things that impressed,

We will never know what men like Cheng Yu saw when Zhang Fei fought alongside (against Lu Bu for example) and against them but one would assume Zhang Fei's feat of arms was highly impressive. However as Liu Bei's forces didn't have a base for most of their careers and the Shu history department was dire, whatever those deeds have slipped through and out of our ever knowing quite what they did.

“You, are a rebellious son who abandoned his father. You are a cruel brigand who murdered his lord. How can Heaven and Earth put up with you for long? And unless you die soon, how can you face the sight of men?”